Question

A ball rolls off the top of stairway with a horizontal velocity of magnitude $1.8 \,m/s$. The steps are $0.20 \,m$ high and $0.20 \,m$ wide. Which step will the ball hit first?

• A. First
• B. Second
• C. Third
• D. Fourth

Answer 1

Answer: (D)

Given, $x=0.20 \,m, y=0.20\, m, u=1.8\, m/s$.
Let the ball strikes the nth step of stairs, Vertical distance travelled
$=n y=n \times 0.20=\frac{1}{2} g t^{2}$
Horizontal distance travelled, $n x=u t$
or $t=\frac{n x}{u}$
$\therefore n y=\frac{1}{2} g \times \frac{n^{2} x^{2}}{u^{2}}$
or $n=\frac{2 u^{2}}{g} \frac{y}{x^{2}}=\frac{2 \times(1.8)^{2} \times 0.20}{9.8 \times(0: 20)^{2}}=3.3 \approx 4$